select the correct answer from each drop - down menu. sharon is assessing the popularity of a fashion…

select the correct answer from each drop - down menu. sharon is assessing the popularity of a fashion magazine for her blog. the number of subscribers to the magazine for the years 2000 to 2004 are given in the table. number of years since 2000 number of subscribers 0 25,000 1 20,000 2 16,000 3 12,800 4 10,240 the number of subscribers is. as the number of years since 2000 increases, the number of subscribers to the magazine will approach. reset next

select the correct answer from each drop - down menu. sharon is assessing the popularity of a fashion magazine for her blog. the number of subscribers to the magazine for the years 2000 to 2004 are given in the table. number of years since 2000 number of subscribers 0 25,000 1 20,000 2 16,000 3 12,800 4 10,240 the number of subscribers is. as the number of years since 2000 increases, the number of subscribers to the magazine will approach. reset next

Answer

Explanation:

Step1: Analyze the data trend

We observe that as the number of years since 2000 increases (from 0 to 4), the number of subscribers decreases from 25000 to 10240. To check if it is an exponential - decay, we find the ratio of consecutive terms. For example, $\frac{20000}{25000}=0.8$, $\frac{16000}{20000} = 0.8$, $\frac{12800}{16000}=0.8$, $\frac{10240}{12800}=0.8$. Since the ratio of consecutive terms is constant ($r = 0.8$), the number of subscribers is decreasing exponentially.

Step2: Determine the limit as years increase

The general form of an exponential - decay function is $y = a\cdot r^{x}$, where $a$ is the initial value and $r$ is the common ratio with $0\lt r\lt1$. As $x$ (the number of years since 2000) approaches infinity, $r^{x}$ approaches 0 when $0\lt r\lt1$. Here, $a = 25000$ and $r = 0.8$. So, as $x$ gets larger and larger, $y=a\cdot r^{x}$ approaches 0.

Answer:

The number of subscribers is decreasing exponentially. As the number of years since 2000 increases, the number of subscribers to the magazine will approach 0.